You should Aajx request to C# controller, with the ID of the row to remove change rank of the item in the database to -1, and decrease the rank of just next row. Suppose You have removed row B with rank 2, then using jQuery Ajax, call C# controller and pass it's Primary Id to the controller, using ADO.NET update it's rank/order value to -1 and decrease rank(from 3 to 2) of just next element(if there is any) like C.

If you don't know how to call Controller fro knockout js take a look at the below code snippet